I would argue the opposite, we live in a world where specialization continues to advance, and that specialization should open the door to polyglot behavior in creating new knowledge. There needs to be more space for researchers to publish half-done research. Personal blogs can be good for this. There needs to be a space for thinking out loud, something less formal than peer review.

Pay-to-publish journals and the collapse of peer review
Peer review is the bedrock of modern science. Without rigorous peer review, by well-qualified reviewers, modern mathematics and science could not exist. Reviewers typically rate a submission on criteria such as:

Relevance to the journal or conference’s charter.

Clarity of exposition.

Objectivity of style.

Acknowledgement of prior work.

Freedom from plagiarism.

Theoretical background.

Validity of reasoning.

Experimental procedures and data analysis.

Statistical methods.

Conclusions.

Originality and importance.

Needless to say, the papers listed above should never have been approved for publication, since such material immediately violates item 7, not to mention items 3, 4, 6 and others. Keep in mind that no editor or reviewer with even an undergraduate degree in mathematics could possibly fail to notice the claim that the traditional value of pi is incorrect. Indeed, it is hard to imagine a comparable claim in other fields: A claim that Newton’s gravitational constant is incorrect? or that atoms and molecules do not really exist? or that evolution never happened? or that the earth is only a few thousand years old?

At the very least, even to an editor without advanced mathematical training, the assertion that the traditional value of pi is incorrect would certainly have to be considered an “extraordinary claim,” which, as Carl Sagan once reminded us, requires “extraordinary evidence.” And it is quite clear that none of the above papers have offered compelling arguments, presented in highly professional and rigorous mathematical language, to justify such a claim. Thus these manuscripts should have either been rejected outright, or else referred to well-qualified mathematicians for rigorous review.

Also, the fervor with which some of these authors address their work should raise a red flag. There is simply no place in modern mathematics and science for fervor in presenting research work (see item #3 in the list of peer review standards above), since any good scholar should be prepared to discard his or her pet theory, once it has been clearly refuted by more careful reasoning or experimentation. Such problems are part of the explanation for the persistence of young-earth creationism, for instance.

So how could such egregious errors of manuscript review have occurred? The present author is regrettably forced to “follow the money” (as the shadowy informant Deep Throat in the movie All the President’s Men recommended). Indeed, all of the above journals listed above are on Beale’s list of pay-to-publish journals. Many of these journals have acquired a reputation of loose standards of publication, with only a superficial review, in return for charging a fee to authors for having their papers published on the journal’s website.